Method of manufacturing cutters



Nov. 21, 1950 E. STAPLES 2,530,549

METHOD OF MANUFACTURING CUTTERS Original Filed Sept. 22, 1943 4 Sheets-Sheet 1 INVENTOR. OT/s' E STAPLE:

ArToe/YEYJ' Nov. 21, 1950 o. E. STAPLES ma'mon OF MANUFACTURING CUTTERS 4 Sheets-Sheet 2 Original Filed Sept. 22, 1943 INVENTOR. 0775 5. 57/2/ 155 4 y AQMdW EW W' ATTORNEY;

0. E. STAPLES METHOD OF MANUFACTURING CUTTERS Nov. 21, 1950 4 Sheets-Sheet 3 Original Filed Sept. 22, 1943 INVENTOR.

Nov. 21, 1950 o. E. STAPLES 2,530,549

METHOD OF MANUFACTURING CUTTERS 4 Sheets-Sheet 4 Original Filed Sept. 22, 1943 h In WW WWW Patented Nov. 21, 1950 UN. 11 ED STAT E'S- PATE OF Fl C E.

2,530,549v METHOD or MANUFACTURING GUTTERS Otis E. Staples, Euclid, Ohio; assignor to The Cleveland. Hobbing Machine Company, Slave.- land, Ohio, a corporation of Ohio.

Continuation of application serrar No: 503,373, September 22, 1943. This application- April;- 22,. 1947, Serial No. 243,055

type employed in machines of the character dis- 1 closed in the aforesaid Carlin patent, were made by a cut and try method, by which method it is impractical to make any but the simplest type of cutters to the accuracy required of modern ma.-

Cursory consideration of. the mat chine tools. ter will show that: the making of a cutter having twoside cutting edges asdistingui'shedfromi. circumferential cutting edges, which sidecutting edges are: required to form shoulders ofai pre.--

determined angles on a work blank and located at. predetermined distances apart, is impractical" by a cut and. try method.

The principal object. of. the present invention. is, therefore, the provision of a scientific: method of accurately laying out or making: cutters. of the type referred to. According to the provisions of the presentinvention, the dimensions of the cutter can bedetermined; with precision, with the result that the design and layout thereof can. beexpedit'ed and the cutters readily manufactured. and reproduced with accuracy.

Further objects and. advantages of the invention reside in the novel steps of procedure employed in producing an. improved cutter of the character: referred to as willbe apparent. to those I skilled in the art to which the invention relates, from the following description or. explanation and the. accompanying drawings forming a. part of this. specification; in which:

Fig. '1 is a diagrammatic view illustrating: that part of the method of the invention whereinxthe cutter is calculated and/or laid out, disregard-- ing the top rake and clearanceangles;

Figs. 2 and 3 are diagrammatic views illustrating the method of determining the corrections to the radii of the arcuate cutting edges shown in Fig. 1 incident to top rake and clearance angles;

Fig. 4 is an enlarged view of a portion of Fig. 3;

Fig. 5 is a diagrammatic view illustrating that part of the method wherein the side clearance angle for the cutting edges which form the shoulders is determined;

Figs- Sand. 7. are diagrammatic views illustratthe shoulder forming. edgesincidentto the toprake angle; and 7 Figse, 9 and. 10 iliustrate a.- method oi grind.- ing. the shoulder forming. edges.

As previously stated; the presentinvention relates to cutters and cams-oi. the character em-- played on. machines. at the type disclosed in. U.

S..Patent No. 2,233,399. Reference to said patent willshow. that the. machine disclosed therein. resembles. a more\ or. less; conventional lathe the details of which. are'not-reproduced. here. It is. suflicient to note that, as diagrammatically rep-= resented. inFig. 1. 0t. thedrawings at this application. the work. blank I 5.is. supper-ted between a chuck (not shownland.a.tail-center 23 of the machine work. blank I5 is turned-to the desired form by a. disk or segment-shaped. tool or cutter T rotatably supported on the tool slide offthe. machine for. rotationabout an axisofiset from. and;v angularly' disposed to the axis of. rotationof. thework. In.operation,= the tool. or cutter is. fed longitudinally of the. axis of. rotation. of. the work blank and-simultaneously rotated in a predetermined. manner at'vari-able speeds by a.

cam G and; camioll-owei; 32 operatively con-- nectedl. thereto by mechanism. comprising a rack 25 and piniont28l. Alternatively. the. work blank: may be moved-relative to the tool or cutter and: cam, etc.,, see: Theodore F1. Garlin-U; S. Patent No.

2,233,398. If desired, theitool '12 may be rotated at. a uniform. rate. of. speed; and the relative movement therebetween and. the work. longitudinally of. the lattereffected at az-variablerate cf speeds or both. of said movementsmay be effected. at variable. rates of. speed; so long; as the. relative angular rotation. of the-tool-T per unit of linear feed is. varied from time to time in a predeterminedimanner- Inpperation, the relative feed: movementsbe-- tween, the tool: and workb1ank-,.that. is the rela tive movementstherebetweem except the; rotation of thework. blank. generally speaking, arev as.

though the. cutter or tool were rolled along: the

work with theresultthat the: respective sun-- faces. of; the work may besaidtobe-generated. by"

the tool. Whenthe relative: feed movements are such thattheeffiectis atrueroiling motion between the arcuately shapedcutting edge of the tool. or cutter andthe section of the finished- 0 work formed. thereby. the cutter ishereim said ing the method of determining the correction for rolling along the work without slip, the cutter 3 is said to be rolled or rolling along the work with underslip. The reverse condition is referred to as overslip.

The present invention is concerned primarily with the method of designing and laying out of cutters of the type referred to for producing articles or work having portions of different diameters connected by shoulders, which shoulders are formed by side cutting edges on the tool or cutter; the cutters as articles of manufacture are disclosed and claimed in my copending divisional application, Ser. No. 38,571, filed on July 14, 1948. In producing workof the nature mentioned, the relative feed movements between the tool or cutter and work are preferably accomplished by rotating the tool or cutter at variable rates of speed and moving the work blank lengthwise at a uniform rate of speed. However, it is to be understood that the tool or cutter may be rotated at a uniform rate of speed and the relative movement between the same and the work blank longitudinally or lengthwise of the axis of rotation of the work blank effected at a nonuniform rate of speed, etc. The cutter and cam combinations must be specifically designed for each differently shaped article to be produced since'the relative angular rotation of the cutter per unit of relative longitudinal movement must be varied in a definite relationship. In other words, each cutter or tool and cam combination is designed for use in connection with a particular machine and the production of a particular article.

The method of the present invention will be described or explained with reference to the design and layout of a cutter and cam for producing an article having a shape which is fairly characteristic of the articles which the machines of the aforesaid Carlin patents are particularly adapted to turn or produce. With the foregoing in mind, it is assumed that it is desired to make a cutter or tool and cam combination for the machine shown in the drawings of Carlin Patent No. 2,233,399 to produce an article 9 having three cylindrical portions or sections I0, II and Hi, the diameters A, B and D of which are 1.000, 1.375 and 1.625 inches, respectively, connected by radial shoulders 13 and M, from a cylindrical work blank l shown in dot-dash lines in Fig. 1, the outside diameter of which blank is the same as the diameter of section 12. I

The first step is to empirically determine one of the following: (1) the offset E, that is the distance between the axis of rotation iii of the tool or cutter and the axis of rotation ll of the work blank measured in the plane oftheaxis of rotation of the work blank normal to the axis of rotation of the tool or cutter; (2) the radius F of the arcuately shapedcutting edge I8 of the tool furthest from the axis of rotation iii of the tool T; or (3) the radius G of the arcuately shaped cutting edge lsnearest the axis of rotation I6 of the tool. These dimensions or distances are optional but when any one is once selected or determined, substantially all the other dimensions of the tool and cam are determined or fixed, and the cutter must be operated at all times in the position determined thereby.

In determining one of the three dimensions referred to above, it must be kept in mind that the radius G of the arcuately shaped cutting edge l9 nearest the axis of rotation I6 of the tool cannot be less than the radius of the hub or like part of the tool, plus any required or desired clearance, and that the radius F of the'cutting edge i 8 must equal G plus one-half the difference between the diameters of the largest and smallest sectionsof the article to be produced. The amount of clearance provided is largely optional but some clearance must be provided to allow for a top rake angle. Other factors that must be considered in determining or selecting the clearance are the characteristics of the machine, cutter sizes which are practical, and practical limitations of offset E. The maximum distance that the arcuately shaped cutting edge I8 of greatest radius can be away from the axis of rotation l6 of the tool is determined by practical limits of so-called overhang consistent with other requirements, such as rigidity, minimization of chatter, etc. The offset E equals the radius of any arcuately shaped cutting edge, plus the radius of the section of work turned thereby.

Having in mind the dimensions aforesaid and the machines of the aforesaid Carlin patents, an offset of 2.500 inches is appropriate and is selected. From the foregoing it follows that 1 -2.500 =2.000 inches B A T =l.8l25 inches The cutter or tool may, if desired, be fed into depth either lengthwise or transversely of the work, but preferably it is rolled into depth. In either event the cutter must clear the blank at the beginning of the operation so that the blank can be readily positioned in the machine. Assumin that the cutter is to be rolled into depth by movements substantially the same as those employed to turn the initial section 10 of the article to be formed, the axis of the cutter must be located beyond the end of the work blank a distance H equal to the base of a right angle, the other sides of which are F and the distance between the axis of the cutter and the outside of the work blank plus some suitable clearance,

7c For convenience, this angle is corrected to the such as 10% of the actual amount required. Having in mind the dimensions given above, it follows that 1.180817 inches If the relative movements between the tool or cutter and work were such that the arcuately shaped cutting edge is extended rolled on the section H] of the work extended, the cutter would rotate through an angle I while the axis thereof traveled to a point 25 a distance H. This angle Angle I=32 27' 34" steam;-

nearestdegreeandhence-an; angle of: 32,? is used;v The mechanism for connecting the camrollenand the tool or cutter? spindle; of necessity, is such that a certain 'oain rise: isnecessary to produce a unit of rotationof;- thertool or cutter or vice versa. This factor of. the. machine is herein designated J, and assuming'that in the instant machine this mechanism is such that a rotation of 1 of they tool r cutter is produced b .03 inch of cam rise; the factor J equals, .03. The cam. rise-K required durin'g thev approach portion'of' the cycle ofoperation', thatis to rotate the'cutter 32, is determined by multiplying 32 by the factor J of the machine, which is assumed to be .03. Therefore K=J' I =.03 321 ==:.960i-nch While the axis of the cutter or tool is traveling from the point 25, in line with the end of the work, to a point 26;. inline with the; shoulder I3} a distance 1. equal to the-length of'the section IQ of the work; which it will be assumed is" 1.500 inches, the cutter is preferably rotated through an angleM sirch that a Slight amount of underslip-occurs, preferably to M is then determinedas follows:

For convenience, 35, the nearest higher: even angleis used.

The cam. rise. N required: to produce this. rotation of the; tool is 35.. times .030: inch-.01 1.05 inches.

The relative movements between the cutter? and work occurring while the section Hi isbeing formed, cannot be continued after the shoulder I3 is formed by the cutting edge 2! connecting the cutting edges or arcs l8 and l9 without destroying the left-hand corner of section II of the work. In order to prevent destruction of this corner, the speed. of rotation of the cutter is accelerated temporarily sufiiciently to. allow the shoulder forming. edge. 21 to clear the shoulder l3, and thereafter continued at a reduced speed buttat a; speed-higher than that atwhi'c'h it was operating during formation ofv the sectiorr Hi. The higher: speedof rotation of the cutter',; during which period overslip is' occurring, preferably continues until the axis of the" cutter reaches. a; point. 24.,- a distance-P from t'her point." 25. While the amountof overslip. effect.- ed. and the distancethrouglr which itv continues depend: uponthe angle. of. the shoulder", etc.', the

amount of overslip efiectedz. preferably about? and the distance. B'through whichgits. is continued is preferably equeli. to; the: length of the shoulder l3, that is one-half the difference between the diameters of the adjacent portions Ill and II, which is .1875 inch.

From the foregoing the" preferred. angle Q through which the cutter is rotated while it is traveling from the point 2'6'to the point 24 is calculated as follows .1875 o me For convenience, an angle; of 8 is used.

The can. rise RI required to: produce" rota.

tion of the: tool when calculated. as" indicated: abovei's zexinch.

While: the. axis of the tool is: traveling" from the. point. 24% to: the point 30; in line with the; shoulder: k4,. a distance- S equal .to r the length. of

the. portion Ll minus; P,.thet cutter is: preferably rotated through anzanglel-Ua Assuming that. the: length of. the. shoulder H is: 1.250. inches, their Sis'equaltci L0625 inches.

The angle U is' preferably suchthat from 10% to; 26%; underslip occurs while: the cutter is? traveling; from: the point 24. to the:- point 30;

Therefore For; convenience,.anangle of. 30 is; employed which-willproduce an: underslip slightly in excess of 10%". The cam riseV requiredto produce this angular rotation of the tool is .9 inch determined as indicated above.

In order to preventdestructionof the outer corner of the shoulder M by. the shoulder forming edge M of the cutter, the; rotation of. the cutter is. again acceleratedin the same. manner as. previously referred. to with. respect. tothe shoulder. l3; The acceleration ispreferabl-y such, thatapproximately 30% overslips occurs. and is. continuedto point 33,.a distance W equal. to;

the height of the shoulder M; which. is-.125:inch-a The: desired angular rotation Xto. be imparted to: the tool during; this movement is calculated.

For convenience, 6 is used. The cam rise Y required to produce this-rotation. is .18 inch calculated as indicated above.

It will be seen, therefore, that" each arcuately shaped cutting edge preferably has a, length which is equal to of the length of the portion of the work to be turned thereby plus approximately of the difference between the radius of that arcuately shaped cutting edge and the radius of the next preceding arcuately shaped cutting edge.

After the cutting operation has been completed, the work blank has to be removed. When possible, the cutter is preferably made segmentlike in shape so that the cutter. can, ineffect, be withdrawn from the work by continuing its rotation for a short period. This-is. accomplished by continuing the feed movement and extending the cam slightly. Any suitable cam rise can be employed depending upon the speed'with which it is desired to have the tool move-clear of the work.

Two of the numerous positions assumed by the cutter or tool as it travels lengthwise: of the work blank areindicated by dot-dash lines in Fig. 1. The reference character 32 designates the cam roller which cooperates with the cam C to effect 75. the rotationof; the cutters. and a rmmber. of?

7 various positions which the roller assumes as it travels along the cam are shown in Fig. 1.

The cutter or tool T is made cylindrical and operated below center, that is, the cutting edges preferably engage the work below the plane 35, see Figs. 3 and 4, of the axis of rotation of the work perpendicular to the axis of rotation of the tool or cutter. In addition, the cutter is provided with a suitable top rake angle C. This arrangement provides the necessary clearance angle even though the periphery of the cutter is cylindrical. The cutting edge of greatest radius is preferably operated slightly below center and the distance that the other edges are below center will depend upon the amount that they are set back with respect to the cutting edge of greatest radius and upon the value of the angle of top rake.

Because the cutter under consideration is to be operated in such a position that the arcuately shaped cutting edges 18, etc. out below the center plane of the work blank, the radii of the cutter previously determined must be increased incident to the curvature of the blank. Preferably the corrected diameters of the arcuately shaped cutting edges are determined in the following manner. An arbitrary radius a not less than F, plus .030 to .050 inch, is assumed as the intersection b of the surface 36, produced by the top rake angle extended, with the plane 35 of the axis of rotation of the work perpendicular to the axis of rotation of the tool. It has been found that with a normal top rake angle a of about 25 this gives about the minimum clearance angle at which the cutting edge of greatest radius can be efficiently operated.

Referring to Figs. 2, 3 and 4, d and e are the corrected radii of the arcuately shaped cutting edges l8 and 19 respectively for producing or turning the sections l and H of the work. Assuming that the top rake angle 0 is 25 and that a equals F+.050 inch, that f is the intersection of the surface 36 of the tool with the cutting edge [8 thereof, that g is the intersection of the plane 35 with the axis of rotation H of the work, and that h, i, and j are the sides of the triangle 1), f, and g opposite the angles 1), f, and g respectively, then Sin ax; b

8 l8 to the axis ll of the work blank is calculated as follows:

k=h cos y =.500X.9989333 =.49946 inch d=E-lc =2.500-.4995 =2.0005 inches The amount 0 to be added to F as the correction incident to the location of the cutting edge l8 below the plane is calculated as follows:

, =.0005 inch The clearance angle m is the same as the angle g or 2 38 As shown in Fig. 4, the angles a, etc. are exaggerated for clearness.

The correction o for radius G is figured in a similar manner and in the example given is .00836 inch. The clearance angle in the case of the cutting edge [9 is then 8 56 30".

The minimum side clearance angle n on the shoulder forming cutting edge 21 is determined by the angle at the point of maximum undercut, that is, the angle at the point where the radially outer end of the shoulder forming cutting edge 2'! undercuts the blank [5 to the greatest extent, see Fig. 5.

The cosine of the angle 1) at which maximum undercut occurs is equal to Z, that is, the distance from the center It of the cutter to the outside diameter of the work blank, divided by G, the radius of the arcuate cutting edge I9 of lesser radius, in other words Cos 12:2

.93103 Therefore,

For convenience, 22 will be employed.

Then the tangent of n, the minimum side clearance angle, is equal to q, the depth of undercut, divided by r, one-half the chord of the circle of outside diameter of the blank at the height of undercut s, or the square root of t times 3 where t is equal to the diameter D of the work blank 15 minus s. The depth of undercut q is equal to the tangent of the angle of maximum undercut multiplied by the length of undercut u, that is, the length of the shoulder forming edge 21.

Expressed mathematically,

q =tan 32 Xu =tan 22 (FG) =.40403(2.0001.8l25) Tan n= r ders must be correctedby an amount equal to angle 1), see Fig '6, to compensate for the effect of top rake and side clearance if the shoulder being formed'is to'be held to a desired predetermined angle.

Assuming that the top rake angle 0 is and that the side clearance angle 11 is 10?, then the tangent of the correction .angle iv for a square shoulder is Tan rv=tanc tanm Therefore,

From the foregoing it .follows that when the shoulder cutting edge is formed as by grinding,

the grinding wheel must be so positioned that the working face thereof makes an angle of 4 :42

with a radial line passing through the intersection of the arcuately shaped cutting edge "of greater radius with the shoulder --cu-tting edge.

The relative positionsof the .cutter'and grinding wheel are shown in Figs. 8, 9 and 10, wherein the reference characters and 4| designate, respectively, a grinding wheel and its axis of rotation.

In the .event that the adjacent cylindrical sections of the blank'are "to be connected bya chamfer or bevel instead @of byaright-angular shoulder, the correction angle for the cutter shoulder forming edge, corresponding with angle '0 above,

is figured in the following manner. Referring to Fig. 7 wherein the parts corresponding with parts previously referred to aredesignatedby the same reference characters with a :;prime mark afiixed thereto, the cylindrical portions '16 and III of the work are connected by ashoul'deror .bevel l3, makingananglew of 459. Hence,

sin

' The angle 9 subtended by the chamfered vor beveledsurface 2.7 of the cutter is as follows:

In the foregoing illustration the uncorrected radii F and-G-were used. Theoretically, thecorrected radii would produce more accurate results. However,:from a practical pointof view the uncorrected radii are satisfactory :since the :error resulting from theusethereof is less than present manufacturing tolerances.

.The equations just derived with respect to Fig. .7 are general andmay beused to deterrnine'the correction angle 12' for the cutting edge of a'tool adapted to forms. shoulderof anypredetermined angle won the work. To facilitate the determination of the angle-v 'itis desirable to express the equation:

in different form. .:Remembering:that:

then

.Cot zsin a tan r an W Since,

and. i

'. cot 2:

Got 2 tan z=tan tan 1:.

Moreover, since Hence, the general equation reduces to the simple form previously given when a square shoulder is to be formed on the work.

When it is desired to form a shoulder on the work having any predetermined angle 10, the setting of the grinding wheel 40 to form the shoulder cutting edge 21' on the tool must be such that the working face of the wheel is inclined to make an angle =4wLv' with a plane extending from the outer edge of the arcuately shaped cutting surface of greater radius perpendicular to a radial line, extending from the axis of the tool through the intersection of the arcuately shaped cutting surface of lesser radius with the shoulder cutting surface. When the shoulder to be formed on the work is square, this inclination of the grinding wheel is simply expressed as being equal to the correction angle measured from the radial line through the intersection of the outer edge of the arcuately shaped cutting surface of greater radius with the shoulder cutting edge, the inclination being in the direction which increases the angle that the shoulder cutting surface makes with the arcuate cutting surface of greater radius.

As will be understood by those skilled in the art to which the invention relates, the work blank, the finished article, the cutter and the cam can be laid out to scale on drawing paper, as indicated on the drawings, and the various dimensions determined graphically with considerable accuracy, and this method of determining the various dimensions is within the scope of the present invention. In order to obtain the to undersip or the or so overslip the various arcuately shaped cutting edges which form the respective portions of the blank are made proportionately shorter or longer than the parts to be finished thereby.

After the cutters have been calculated and/or laid out in the manner described, they may be rough formed by conventional equipment in any suitable manner, hardened, and then ground to final size and shape, The side or shoulder cutting edges can be ground by employing a conventional grinding machine having a fiat faced grinding wheel, means to produce a linear feed betweenthe wheel and the work, and a work support which may be adjusted to present the work to the face of the grinding wheel at the angles determined as described above.

From the foregoing explanation it will be apparent that the objects of the invention her ofore illustrated have been accomplished and that a new and improved method of making a cutter has been devised. While the invention has been described in considerable detail, it will be apparent that certain changes may be made within the scope of the invention, and it is my intention to hereby cover all adaptations, modifications and uses of the invention disclosed herein.

Having thus described my invention, I claim: 1. The method of laying out and making a disk or sector-like tool or cutter having radially offset arcuately shaped cutting edges along one side of the circumference connected by a side cutting edge or edges, which cutter is adapted to turn an article having cylindrical sections connected by a shoulder or shoulders when rotated in cutting relationship with a rotating work blank at variable speed about an axis offset from and angularly disposed with respect to the axis of rotation of the work blank while a relative feed movement is efiected between the cutter and work blank lengthwise of the work blank, which method comprises: selecting the radius of one of the arcuately shaped cutting edges of the cutter taking into consideration characteristics of the machine upon which the cutter is to be used, practical limitations upon the size of the cutter, permissible overhang of the cutting edge farthest from the axis of rotation of the cutter, and calculating the radius of the other arcuately shaped cutting edge or edges in accordance with the selected radius and the differences between the radii of the respective cylindrical portions of the article to be turned by the edges; selecting the lengths of the arcuately shaped cutting edges for turning the respective cylindrical portions of the work taking into consideration the usable circumierence of the cutter, the speed of rotation of the cutter, the acceleration or deceleration re quired to clear the shoulder or shoulders to be produced; selecting the top rake angle or angles; determining the front clearance angle or angles for said arcuately shaped cutting edges and providing therefor; determining the side clearance angle or angles for the shoulder forming cutting edge or edges equal to or greater than the angle whose tangent is equal to the depth of undercut divided by one-half the chord of the circle of outside diameter of the work blank at the height of undercut; providing a blank of approximately the desired final form and size; effecting relative rotation between the blank and a grinding wheel supported in cutting relationship about the axis of the blank to form the arcuately shaped sides of the blank; and effecting relative movement between the blank and a grinding wheel supported in cutting relationship in a direction inclined to the axis of rotation of the blank at an angle substantially equal to the desired clearance angle for the shoulder cutting edge with the working face of the grinding wheel inclined to a plane, extending from the outer end of the shoulder cutting edge of the completed cutter perpendicularly to a radial line thereof extending through the intersection of the shoulder cutting edge with the arcuately shaped side of the completed cutter having the lesser radius at an angle substantially equal to (QT-4e), where Got 2:

Sin

c =top rake angle .n side clearance angle.

' or sector-like tool or cutter having radially offset arcuate'ly shaped cylindrical portions provided with cutting edges along one side orend connected by a side cutting edge or edges, which tool is adapted to turn :an article havingcylind-rical sections connected by a shoulder or shoulders when relatively rotated in cutting relationship with a rotating work blank at variable speed about an axis offset from and angularly disposed with respect to the axis of rotation of the work blank with the cutting edges of the tool cutting .below the plane of the axis of the work blank perpendicular to the axis of the tool while a relative ieed movement is effected between the tool and work blank'lengthwise of the work blank, which method comprises: selecting the radius of one of themcuately shaped cutting edges of the tool taking into consideration characteristics of the machine upon which the tool is to be used,practical limitations upon the size of the tool, permissible overhang of the cutting edge farthest from the axis of rotation of the tool, and determining the .radius of the other arcuately shaped cutting edge or edges with respect thereto; selecting the anglessubtended by the respective arcuately shaped cutting edges for turning the various cylindrical portions .of the work taking into consideration the usable circumference .of the tool, the speed of rotation of the tool, theacceleration or deceleration to be given the tool in clearing the shoulder er shoulders "to be formed; selecting the top -rake angle or angles; correcting the radii of the various arcu'a'tely shaped cutting edges incident :to their location below the plane of the axis of rotation of the work blank perpendicular to the axis of rotation of the tool: determinin "the side clearance angle or angles for the shoulder form-- ing cutting edge or edges equal to or greater than the angle whose tangent is equal. to the depth of undercut divided by one-half the chord of the circle of outside diameter of the work blank at the height of undercut; providing a blank-oi approximately the desired final form and size; effecting relative rotation between the blank and a grinding wheel supported in cutting relationship about the axis of the blank to form the arcuately shaped cylindrical portions of the tool;

and effecting relative movement between the blank and a grinding wheel supported in cutting "relationship in adirection inclined to the axis of rotation of the blank at an angle substantially equal to the desired clearance angle for the side cutting edge with the working face of the-grinding wheel inclined to a plane, extending from the outer end of the side cutting edge of the-completed tool perpendicularly :to a :radial line-of the tool extending through the intersection of vthe side cutting edge with the .arcuatelyshaped cylindrical portion of the 'tool having the lesser radius at an angle approximately equal to (90 [2) where Got 2:

F-=radius of the adjacent arcuate cutting edge farthest from the axis of rotation oi' the =too'1 y=i18.0"--the angle :offlthe shoulder to be formed Y van i=4 3 1/ c"=t'op rake angle -n =side. clearance rangle.

3.. 'llhe method of making .a disk :or sectorlike tool :or butter provided with stop :rake and having radially fofiset .ai'cuately shaped cylindrical pontions provided with cutting edges along one side 101 end nonnected by a side cutting edge, which 130.01 is adapted to turn an article having ccylindrical sections connected by a shoulder when motated :in cutting relationship with is rotating work blank :at variable speed about an axis onset from :and angularly disposed with respect to the axis of rotation of the-work blank while ;:a relative feed movement is effected between the tool and work blank lengthwise of the work, which method comprises: providing a blank .of approximately the desired final form :or shape; eiiectingrelative rotation between the blank and a :griding wheel supported in rout-ting relationship about the axis of rotation of the blank to form the arcuately shaped cylindrical portions; subsequently grinding the side cutting edge including a clearance angleby efiecting relative movement between the blank and a grinding wheel supported in "cutting relationship in a path inclined to the axis of IO- tation of the blank at an angle substantially-equal to the desired clearance angle of the side'cutting edge with the working face of the grinding wheel 'inclined'to a plane, extending from the outer end of the sidecutting edge 01' the tool perpendicularly to a radial line of the "tool extending through the intersection of side cutting edge with the arcuate'ly shaped cylindrical portion of "the tool having the lesser radius atan angle-approximately equal-to wo 12}, where =top rake angle "n" =side clearance angle.

"4. The .method of laying out and making -.a disk or sector-like nutter having sradially offset arcuately shaped cutting edges along one :side :of' the circumference connected by .a :side cutting ledge-or edges, which cutter is adapted to turn an article :haviing cylindrical sections-connected. by :a shoulder or shoulders :when rotated :in cutting relationship with a, rotating work blank at variable speed about an axis offset from and angularly disposed with respect to the axis of rotation of the work blank while a relative ifeed movement :is yefiected between :the cutter andwork blank :lenjgthwise zof'ithe work :blan'k, which :method comprises: providing a lblank:.-;oi

. approximately the desired :final form and seize;

effecting relative rotation between the blank and :a grinding wheel about the axis of the "blank to form one of the arcuately shaped side portions of the cutter to a predetermined radius; effect.- .ing relative rotation between-the "blank and .a grinding wheel supported in cutting relationship about the axis of the thlankxto form another of thetarcuatelyis'haped side portions of :the putter to .a radius determined with respect to the firstmentioned vradius and differing therefrom inversely as the diameters of the parts to be turned thereby differ from each other; and forming the side cutting edge or edges by effecting relative movement between the blank and a grinding wheel supported in cutting relationship in a direction inclined to the axis of rotation of the blank at an angle substantially equal to the desired clearance angle of the side cutting edge being formed with the working face of the grinding wheel inclined to a plane, extending from the outer end of the side cutting edge of the completed cutter perpendicularly to a radial line of the cutter extending through the intersection of the side cutting edge with the arcuately shaped side portion of the cutter having the lesser radius, at an angle approximately equal to (SIP-'42:), where F =radius of the adjacent arcuate cutting edge farthest from the axis of rotation of the cutter Got 2:

G :rad ius of the adjacent arcuate cutting edge nearest to the axis of rotation of the cutter y=180the' angle of the shoulder to G sin y be formed =top rake angle n =side clearance angle.

axis oiiset from and angularly disposed with respect to the axis of rotation of the work blank while a relative feed movement is efiected between the cutter and work blank lengthwise of the work blank, which method comprises: providing a blank of approximately the desired final form and size; efiecting relative rotation between the blank and a grinding wheel about the aXis of the blank to form one of the arcuately shaped cylindrical portions of the cutter to a predetermined radius taking into consideration char- "acteristics of the machine upon which the cutter is to be used, practical limitations upon the size of the cutter, and permissible overhang of the cutting edgefarthest from the axis of rotation of the cutter; effecting relative rotation between the blank and a grinding wheel about the axis of "the blank to form another of the arcuately shaped cylindrical portions of the cutter to a radius difiering from the first-mentioned radius inversely as the diameters of the parts to be turned thereby differ from each other; and forming the side cutting edge or edges by efiect- Ting relative movement between the blank and a grinding wheel supported in cutting relationship in a direction inclined to the axis of rotation of the blank at an angle substantially equal to the desired clearance angle of the side cutting edge being formed with the working face of the grinding wheel inclined to a plane, extending from the outer end of the side cutting edge of the 'completed cutter perpendicularly to a radial line 'of the cutter extending through the intersection of the side cutting edge with the arcuately shaped cylindrical portion of the cutter havi F =radius of the adjacent arcuate cutting edge farthest from the axis of rotation of the cutter G =radius of the adjacent arcuate cutting edge nearest to the axis of rotation of the cutter y=l-the angle of the shoulder to be formed Cot 2 G" sin y F! c'=top rake angle or =side clearance angle 6. The method of forming a cutter tool for a machine tool comprising: providinga substantially cylindrically-shaped tool blank; forming an arcuately shaped cutting surface on said blank having a radius of a value determined from the finished diameter of the work to be cut thereby andthe mode of operation of the tool; forming a second arcuately shaped cutting surface on said tool blank having a radius difiering from the radius of the first-mentioned cutting surface by an amount approximately equal to one-half the difference between the diameters of the work to be, turnedby the two surfaces; providing the arcuatel shaped cutting surfaces with top rake Sin x= having an angle determined from the mode of operation of the tool; and forming a, shoulder cutting surface on the portion of the tool blank uniting the two arcuately shaped cutting surfaces by removing material by relative movement between the blank and a material removing means supported to effect material removal in a path in.- clined to the axis of rotation of the tool at an angle substantially equal to the desired clearance F =radius of the arcuate cutting surface of the tool having the greater radius G"'=radius of the arcuate cutting surface of the tool having the lesser radius .y=l80-the angle of the shoulder to be formed 0 the work G sin y F! c =top rake angle Sin x= n=side clearance angle.

7. The method of forming a cutter tool for a machine tool comprising: providing a substantially cylindrically-shaped tool blank; forming an arcuately shaped cutting surface on said blank having a radius of a value determined from the finished diameter of the work to be out thereby and the mode fo operation of the tool; forming a second arcuately shaped cutting surface on said tool blank having a radius differing from the radius of the first-mentioned cutting surface by an amountapproximately equal to one-half the difference between the diameters of the work to be turned by th two surfaces; providing the l7 arcuatelyshaped cutting surfaces with top rake having an angle determined from the mode of operation of the tool; and forming a shoulder cutting surface on the portion of the tool blank uniting the two arcuately shaped cutting surfaces by removing material therefrom by relative movement between the blank and a material removing means supported tof efiect material removal in a path inclined to the axis of rotation of the tool blank at an angle substantially equal to the desired clearance angle of the shoulder cutting surface and at an angle 2 with the radial line through the intersection of the shoulder cutting edge with the arcuately shaped cutting surface of greater radius, where Tan z=tan 0' tan In 18 c'=the top rake angle n=the side clearance angle.

OTIS E. STAPLES.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date 1,540,757 Buckingham June 9, 1925 1,815,324 Olson July 21, 1931 1,882,692 Albertson Oct. 18, 1932 2,010,353 Edgar Aug. 6, 1935 2,233,399 Carlin Mar. 4, 1941 2,341,668

Staples Feb. 15, 1944 

